Determining clock models

ABSTRACT

Examples disclosed herein relate to methods and apparatuses for observing signals transmitted by one or more transmitters in an asynchronous communication network and applying a time reference to generate a clock model. In one embodiment, parameters representing the clock model may then be forwarded to other mobile devices to assist in positioning operations.

CROSS REFERENCE TO RELATED APPLICATIONS

This application is a divisional of, and claims the benefit of priorityfrom, U.S. patent application Ser. No. 13/418,068, entitled “DeterminingClock Models,” filed Mar. 12, 2012, which such application isincorporated by reference herein.

BACKGROUND

1. Field

The subject matter disclosed herein relates to determining and applyingfine time parameter(s) of a clock model.

2. Information

Wireless position determination systems may be used to determine thelocation of a device. The device may be a mobile or portable device thatoperates on battery power. A mobile handset may obtain a position fix byprocessing signals received from terrestrial transmitters fixed at knownlocations using any one of several techniques such as, for example,advanced forward trilateration (“AFLT”) and/or observed time differenceof arrival (“OTDOA”). In these particular techniques, a range from amobile device receiver may be measured to three or more of suchterrestrial transmitters fixed at known locations based, at least inpart, on pilot signals transmitted by the transmitters fixed at knownlocations and acquired at the mobile device receiver. A mobile devicemay compare an observed phase of a pilot signal received from a knowntransmitter with a time reference to measure a range to the transmitterusing known techniques. Unfortunately, a pilot signal transmitted from abase station is typically not precisely synchronized with such a timereference. This may happen, for example, if the pilot signal istransmitted from an “asynchronous” wireless communication network. Thismay lead to inaccurate measurements of ranges to terrestrial basestations based upon observed phases of such pilot signals.

SUMMARY

In one implementation, a method comprises: receiving from each of one ormore mobile devices fine time measurements determined based, at least inpart, on a first time reference in one or more first signals received atthe mobile device from an asynchronous network and a second timereference; computing a clock model descriptive of timing of at least onesignal transmitted from a transmitter in the asynchronous network based,at least in part, on the fine time measurements; and transmittingparameters representative of the computed clock model to other mobiledevices.

In another implementation, an apparatus comprises: a receiver to receivemessages from a communication network; a transmitter to transmitmessages to said communication network; and a processor to: compute aclock model descriptive of timing of at least one signal transmitted inan asynchronous network based, at least in part, on fine timemeasurements received in messages from each of one or more mobiledevices, said fine time measurements being determined based, at least inpart, on a first time reference in on or more first signals received atthe mobile device from the asynchronous network and a second timereference; and initiating transmission of messages containing parametersrepresentative of the computed clock model through the transmitter toother mobile devices.

In another implementation, an article comprises: a storage mediumcomprising machine-readable instructions stored thereon which areexecutable by a special purpose computing apparatus to: compute a clockmodel descriptive of timing of at least one signal transmitted in anasynchronous network based, at least in part, on fine time measurementsreceived in messages from each of one or more mobile devices, said finetime measurements being determined based, at least in part, on a firsttime reference in one or more first signals received at the mobiledevice from the asynchronous network and a second time reference; andinitiating transmission of messages containing parameters representativeof the computed clock model to other mobile devices.

In another implementation, an article comprises: a storage mediumcomprising machine-readable instructions stored thereon which areexecutable by a special purpose computing apparatus to: compute a clockmodel descriptive of timing of at least one signal transmitted in anasynchronous network based, at least in part, on fine time assistancemeasurements received in messages from each of one or more mobiledevices, said fine time measurements being determined based, at least inpart, on a first time reference in one or more first signals received atthe mobile device from the asynchronous network and a second timereference; and initiating transmission of messages containing parametersrepresentative of the computed clock model to other mobile devices.

In another implementation, an apparatus comprises: means for receivingfrom each of one or more mobile devices fine time measurementsdetermined based, at least in part, on a first time reference in one ormore first signals received at the mobile device from an asynchronousnetwork and a second time reference; means for computing a clock modeldescriptive of timing of at least one signal transmitted from atransmitter in the asynchronous network based, at least in part, on thefine time measurements; and means for transmitting parametersrepresentative of the computed clock model to other mobile devices.

In another implementation, a method comprises, at a mobile device:observing signals transmitted by one or more transmitters in anasynchronous communication network; updating a clock model based on atleast one time reference in at least one of the observed signals; andapplying the updated clock model to an acquired signal transmitted fromat least one of the transmitters to obtain a position fix at the mobiledevice based, at least in part, on the updated clock model.

In another implementation, an article comprises: a non-transitorystorage medium comprising machine-readable instructions stored thereonwhich are executable by a special purpose computing apparatus to:observe signals transmitted by one or more transmitters in anasynchronous communication network; update a clock model based on atleast one time reference in at least one of the observed signals; andapply the updated clock model to an acquired signal transmitted from atleast one of the transmitters to obtain a position fix at a mobiledevice based, at least in part, on the updated clock model.

In another implementation, an apparatus comprises: a receiver to acquiresignals transmitted in an asynchronous communication network; and aprocessor to: observe signals acquired at said receiver and transmittedby one or more transmitters in an asynchronous communication network;update a clock model based on at least one time reference in at leastone of the observed signals; and apply the updated clock model to anacquired signal transmitted from at least one of the transmitters toobtain a position fix at a mobile device based, at least in part, on theupdated clock model.

An apparatus comprising: means for observing signals transmitted by oneor more transmitters in an asynchronous communication network; means forupdating a clock model based on at least one time reference in at leastone of the observed signals; and means for applying the updated clockmodel to an acquired signal transmitted from at least one of thetransmitters to obtain a position fix at the mobile device based, atleast in part, on the updated clock model.

BRIEF DESCRIPTION OF THE FIGURES

Non-limiting and non-exhaustive examples will be described withreference to the following figures, wherein like reference numeralsrefer to like parts throughout the various figures.

FIG. 1 is a schematic diagram of a communication network according to animplementation.

FIG. 2 is a flow diagram of a process to determine parameters of acomputed clock model according to an implementation.

FIG. 3 is a plot illustrating a relationship between asynchronousnetwork time and GPS time according to an implementation.

FIG. 4 is a flow diagram of a process to apply an updated clock model inobtaining a position fix according to an implementation.

FIG. 5 is a plot illustrating a relationship between network frames andtime according to an implementation.

FIG. 6 illustrates a growing uncertainty in an estimated time accordingto an implementation.

FIG. 7 is a schematic diagram of a mobile device according to animplementation.

FIG. 8 is a schematic diagram of a network computing environmentaccording to an implementation.

DETAILED DESCRIPTION

The Global Positioning System (“GPS”) and other like satellitepositioning systems (SPSs) have enabled navigation services for mobilehandsets in outdoor environments. Global navigation satellite systems(“GNSS”), such as the GPS, Galilleo, GLONASS and the like, may enable aterrestrial navigation receiver to process one or more SPS signalstransmitted from transmitters fixed to space vehicles (“SVs”) to obtainpseudorange measurements from the navigation receiver to thetransmitters. With pseudorange measurements to a sufficient number oftransmitters and knowledge of locations of the transmitters, thenavigation receiver may estimate its location. An SPS signal may beencoded with a repeating sequential code. In one implementation, areceiver may attempt to determine a pseudorange measurement from anacquired SPS signal based, at least in part, on a detected code phaseassociated with the acquired SPS signal using well known techniques.

While a location estimate of a mobile device or “position fix” obtainedfrom processing SPS signals is typically very accurate, use of SPSsignals to obtain such a location estimate is not always available. Inurban environments or canyons, for example, SPS signals may undergomultipath and/or attenuation making it difficult to process thesesignals to obtain pseudorange measurements. Also, obtaining a positionfix by processing received SPS signals typically consumes substantiallymore battery energy/battery life than obtaining a position fix usingOTDOA and/or AFLT. Also, some mobile handsets have receivers withcapabilities limited to merely processing signals transmitted fromterrestrial communication networks (e.g., cellular communicationnetworks).

Alternatively, a mobile handset may obtain a position fix by processingpilot signals received from terrestrial transmitters fixed at knownlocations using any one of several techniques such as, for example, AFLTand/or OTDOA mentioned above. In these particular techniques, a rangefrom a mobile device receiver may be measured to three or more of suchterrestrial transmitters fixed at known locations based, at least inpart, on phase detections in acquired pilot signals. A mobile device maycompare an observed phase of a pilot signal received from a knowntransmitter with a time reference to measure a range to the transmitterusing known techniques. However, a pilot signal transmitted from a basestation may not precisely synchronized with such a time reference. Thismay happen, for example, if the pilot signal is transmitted from an“asynchronous” wireless communication network. In this context, atransmitter in a “synchronous network” as indicated herein is directedto a device that transmits a signal modulated by a time reference thatis synchronized with a known clock. For example, GPS, or other GNSS, maytransmit a signal that is modulated with a data signal comprising a timereference that is synchronized with a GPS clock. Also, certain cellularcommunication systems such as CDMA, for example, are synchronized with aknown clock. In contrast, a receiver may acquire a signal transmittedfrom an “asynchronous network” having a timing reference that is notsynchronized to a clock that is known by the receiver. Certain cellularcommunication systems including, for example, GSM and WCDMA, may appearto a mobile receiver as asynchronous. Here, detection of a timingreference in a signal from a transmitter in an asynchronous network maybe of limited use in attempting to measure a range to the transmitterbased on a measured signal travel time without knowledge of arelationship between timing of the signal in the asynchronous network.

In one particular implementation, mobile devices operated by subscribersin an asynchronous communication network may assist in development of aclock model for modeling timing (e.g., a reference time) of signalstransmitted from particular transmitters (e.g., base stationtransmitters) in the asynchronous network. Parameters representing adeveloped or updated clock model may then be transmitted to subscriberdevices in the asynchronous network and/or other devices. By having anaccurate clock model for modeling timing of signals transmitted fromparticular transmitters in an asynchronous network, a mobile device maybe better capable of obtaining accurate pseudorange measurements to theparticular transmitters by compensating for relative time offsets ofsignals transmitted by the particular transmitters to a reference timeframe.

FIG. 1 is a schematic block diagram of a communications network 100comprising first mobile devices 112 and second mobile devices 116.

Communications network 100 may comprise a cellular communicationsnetwork capable of enabling voice or data communication for a number ofmobile devices including first mobile devices 112 and second mobiledevices 116.

FIG. 1 illustrates a particular implementation in which mobile devices(e.g., first mobile devices 112 and second mobile devices 116) in anasynchronous network may act as either gatherers of timing events and/orconsumers of a clock model derived from crowdsourced timing events.First mobile devices 112 may acquire signals from a synchronous networksuch as a satellite positioning system (e.g., GPS) and signals from oneor more base station transmitters of an asynchronous network. Firstmobile devices 112 may then compare an observed timing event in a signalacquired from a transmitter in the synchronous network with a timingreference in a signal acquired from a transmitter in an asynchronousnetwork to derive fine time assistance parameters. Fine timemeasurements obtained at one or more mobile devices (first mobile device112, second mobile device 116, etc.) in the asynchronous network maythen be transmitted to a server for computing a “crowdsourced” clockmodel descriptive of a time reference in signals transmitted bytransmitters in the asynchronous communication network.

Communication network 100 may include a first server 102, a secondserver 106, a network 104, a wireless network 108, SVs 110, and basestations 114. Communications network 100 may include numerous basestations 114 that enable mobile devices such as mobile devices 112 and116 to access wireless network 108. Base stations 114 may be grouped orcategorized based on geographic data, historical data, predictivepatterns, traffic flow, or any combination thereof. The particularconfiguration of base stations depicted in FIG. 1 is merely an exampleconfiguration and claimed subject matter is not limited in this respect.

SVs 110 may be associated with one or more GNSS' such as, GPS, GLONASS,and Galileo, although the scope of claimed subject matter is not limitedin this respect. First mobile devices 112 and/or second mobile devices116 may acquire signals transmitted from satellites 110 to, among otherthings obtain a position fix.

In another aspect, position determination calculations may be performedby a network entity such as, for example, a first server 102 and/orsecond server 106, rather than at a first mobile device 112 and/orsecond mobile device 116. Such a calculation may be based, at least inpart, on signals acquired by first mobile device 112 and/or secondmobile device 116 from one or more of base stations 114. In a furtheraspect, first server 102 and/or second server 106 may transmit thecalculated position to first mobile device 112 and/or second mobiledevice 116.

First server 102 may be connected to (communicate with) second server106 via network 104 and connected (communicate with) first mobile device112 and/or second mobile device 116 via wireless network 108. Inparticular implementations, network 104 and wireless network 108 mayfacilitate communication with Internet Protocol packets. However, othercommunication formats may be used. First server 102 may utilize a firstcommunication link 118 to transmit assistance messages to first mobiledevices 112 via wireless network 108. Second server 106 may utilize asecond communication link 120 to transmit assistance messages to secondmobile devices 116 via wireless network 108. A first mobile device 112may utilize a third communication link 112 to transmit messagescontaining fine time measurements to first server 102 and/or secondserver 106 via wireless network 108.

In one embodiment, fine time measurement(s) may be determined based on,for example, observed event signals received from an asynchronousnetwork (such as observed signal frame boundaries) and time stamps insignals received from a synchronous network (e.g., synchronous cellularcommunication network or SPS) from one or more mobile devices 112. In aparticular implementation, fine time measurements may comprise anindication of an observed offset or time difference between a first timereference in a signal transmitted in a base station of an asynchronousnetwork and a second time reference reliably synchronized with a knownclock (e.g., time reference in an SPS signal).

In a particular implementation, server 102 or 104 may combine orcrowdsource fine time measurements obtained at and received frommultiple mobile devices 112 in determining a clock model for aparticular base station transmitter in an asynchronous network. Here,observations of signals transmitted from a base station in anasynchronous network from multiple mobile devices 112 may enablecomputation of clock model with greater accuracy than a clock modelcomputed based observations from a single mobile device 112.Additionally, as discussed herein, accuracy of fine time measurementsdetermined from observations at a mobile device 112 may be affected byaccuracy of an estimated location of the mobile device 112 and accuracyof an estimated time. Accordingly, fine time measurements received frommultiple mobile devices 112 may be appropriately weighted according tohow accurately location and time are known while signals from anasynchronous network are being observed.

In one implementation, to account for signal propagation time inobtaining or referencing fine time measurements, an accurate comparisonof an observed timing reference in a signal acquired from a synchronousnetwork with a timing reference observed in a signal acquired from anasynchronous network may consider a location of an observing mobiledevice. As such, accuracy of fine time measurements obtained at a mobiledevice may depend, at least in part, on an uncertainty of a location ofthe mobile device and an uncertainty in time (e.g., as synchronized witha GPS clock). Accordingly, fine time measurements obtained from mobiledevices 112 with a high time or position uncertainty may be given a lowweight, or ignored altogether in computing a clock model.

In a particular implementation, a clock model derived from crowdsourcedfine time measurements may be capable of predicting behavior of thetiming of asynchronous network signals in the future. This may allow forless frequent requests for positioning assistance data (e.g., for use ofAFLT in an asynchronous network). A mobile device may be able to enhanceand update a provided clock model based on its own observation ofnetwork signals or events, and may extend usage further to reducerequests for positioning assistance data.

As pointed out above, acquisition of signals transmitted by atransmitter in an asynchronous network at a mobile device may be oflittle utility in measuring a range to the transmitter based on ameasured transmission time. FIG. 2 is directed to a process 120 ofdetermining a clock model descriptive of timing of one or more signalstransmitted by an asynchronous network. This computed clock model maythen be distributed among mobile devices for use in positioningoperations such as, for example, measuring a range to a transmitter inan asynchronous network.

At block 122, a server (such as first server 102) may receive fromindividual mobile devices (such as mobile devices 112) messagescontaining fine time measurements to enable one or more servers (e.g.,servers 102, 106) to compute assistance parameters to be forwarded to amobile device (e.g., mobile devices 116). As described below in specificimplementations, a mobile device (e.g., a mobile device 112) may obtainfine time measurements from observing signals transmitted from bothsynchronous networks (e.g., GPS or CDMA) and signals transmitted fromasynchronous networks (e.g., GSM, WCDMA or LTE). Here, a mobile devicemay determine a fine time measurement based, at least in part, on afirst time reference in one or more signals received from a transmitterin an asynchronous network and a second time reference. In oneimplementation, the second time reference may be reliably synchronizedwith a known clock such as, for example, a GPS clock (or clock foranother like SPS) or a clock for a synchronous cellular communicationnetwork, just to name a couple of examples. In a particularimplementation, a particular network may appear to a mobile device asbeing synchronous or asynchronous depending on whether the mobile devicehas knowledge of a clock that is advancing timing of the particularnetwork. In one embodiment, a mobile device may be pre-programmed todistinguish between an asynchronous network and a synchronous networkbased on a particular receiver or transceiver used for observing asignal in question (e.g., synchronous if the observed signal is beingprocessed/acquired at a GPS or CDMA interface and asynchronous if theobserved signal is being processed/acquired on a GSM or WCDMAinterface). Also, in particular implementations, the mobile device mayinternally maintain the second time reference using an internal clockthat is updated from time to time from acquisition of signals with atime reference (e.g., transmitted by a synchronous network).

Particular examples described below identify GPS or an SPS hascomprising a synchronous network. It should be understood, however, thatthese are merely examples of a synchronous network and claimed subjectmatter is not limited in this respect. In one particular implementation,a mobile device may determine fine time measurements including frameboundaries detected in a signal acquired from an asynchronous networkand time references detected in an acquired GPS signal. A base stationtransmitter in an asynchronous network may continuously generate messageframes and transmit signals based on an internal clock. In the absenceof GPS time stamps on these frames, their temporal relationship to theGPS time may be ambiguous and arbitrary. Furthermore, there may exist aninherent ambiguity from frame to frame since a frame number may reset tozero after reaching a maximum value. This may be referred to as “framerollover” event happening every 3.48 hours in GSM and 40.96 seconds inWCDMA, for example.

According to an embodiment, and as discussed below, a continuous timemodel may be constructed from observed network frames despite frameambiguity and frame rollover. FIG. 3 illustrates a particular example ofusing a time reference observed in a GPS signal to construct acontinuous time model for an asynchronous network. However, this ismerely an example of a signal having an observable time reference thatis reliably synchronized to a known clock, and claimed subject matter isnot limited in this respect. As illustrated in a particular exampleshown in FIG. 3, a time reference point may be established within a GPSweek which is the head of a first frame of a first frame rollover periodin the asynchronous network in the GPS week. Here, point 130 may mark areference network time point for a week i and beginning of a fine timemeasurement observation while point 134 may mark a referenceasynchronous network time for a week i+1. A number of frame rolloverevents for a given measurement (frame number, GPS time) may be obtainedbetween points 130 and 134. A corresponding number of frames may beadded to a reported frame number. An observed network frame number maybe converted to seconds by multiplying the network frame number byseconds/frame (e.g., 4.615 ms/frame in GSM and 10.0 ms/frame in WCDMA).An artificial time offset may be removed by subtracting an initialoffset value at the beginning of the observed week to align asynchronousnetwork time and GPS time at the beginning of the observed week. Line131 may represent an advance of time according to GPS time while line133 may represent an advance of time according to an asynchronousnetwork. A difference between asynchronous network time and GPS time maybe observed at 132. A previous time offset may be added for continuityif there is an existing estimate of relative time offset from a previousweek. This difference between network time and GPS time may then beincluded in fine time measurements to be transmitted to a server asdiscussed above.

In one particular non-limiting example implementation, a fine timemeasurement obtained at a mobile device may comprise a frame numberobserved in a signal received from a transmitter in an asynchronousnetwork (fn) and a time that the frame number was observed (e.g., GPStime). Also, an estimated location, along with an uncertainty of theestimated location of the mobile device, may also accompany the finetime measurements. A message containing a fine time measurement mayinclude the observed frame number, estimated location and uncertainty,and GPS time as a time stamp.

At block 124 of FIG. 2, a server may compute a clock model descriptiveof timing of signals transmitted from one or more transmitters (e.g.,base station transmitters) in an asynchronous network based, at least inpart, on fine time measurements obtained in block 122 (e.g., differencebetween asynchronous network time and GPS time in the particularnon-limiting example above). In a particular implementation, parametersto model timing of a base station transmitter may be computed inexpressions (1) and (2) as follows:

b(t _(i))=b(t _(n−1))+∫_(t) _(n−1) ^(t) ^(i) Δf(t)dt≈b(t _(n−1))+(t _(i)−t _(n−1))Δf(t _(n−1));  (1)

m(t _(i))=b(t _(i))+e _(b)(t _(i))≈b(t _(n−1))+(t _(i) −t _(n−1))Δf(t_(n−1))+e _(b)(t _(i))  (2)

where:

b(t) is a relative time offset between asynchronous network time and atime reference reliably synchronized with a known clock (e.g., GPS timereference) in sec;

Δf(t) is a normalized frequency offset of a clock controlling theadvance of time in an asynchronous network in ppb (part per billion);

m(t) is a relative time offset measurement between asynchronous networktime and the time reference reliably synchronized with the known clockin sec; and

e_(b)(t) is a measurement error on clock offset from the mobile andassumed to be zero mean independently and normally distributed.

Values for m(t) may be determined from fine time assistance measurementsreceived from one or more mobile devices. First, a frame number fn maybe converted to continuous units of time (as described below). Thedifference between this continuous time and a time that the frame numberwas observed (e.g., GPS time stamp provided in the message containingthe fine time measurement) may then provide a value for m(t). A value ofb(t) may then be computed based on m(t) by, for example, removal of anyknown measurement biases. A value for Δf(t) represents a frequencyoffset of a clock controlling the advance of time in signals transmittedfrom the asynchronous network in question and may be estimated based onan observed drift in m(t) and/or b(t). By estimating a value for Δf(t),a value for b(t) may be predicted as shown above.

In a particular implementation, the advance of time in an asynchronousnetwork may be controlled by an internal clock. For example, a timereference in a signal transmitted in an asynchronous network may becontrolled by an internally maintained clock (e.g., internallymaintained clock at a base station). As such, a drift in frequency ofthe internally maintained clock may impart a drift in the time referencein the signal transmitted in the asynchronous network. As may beobserved from expressions (1) and (2), following an updated measurementof b(t) and Δf(t) obtained, for example, from fine time measurementsreceived from mobile devices in block 122, expressions for computingb(t) and Δf(t) may be updated or predicted based, at least in part, onm(t) which is calculated from fine time measurements from mobiledevices.

In a particular implementation, mobile devices may provide fine timemeasurements to a server for computation of a clock model in messagesthat batch several fine time measurements over a time period of adifference between asynchronous network time and a time referencereliably synchronized with a known clock over a time period. As such,parameters of a clock model descriptive of timing of signals transmittedfrom one or more transmitters (e.g., base station transmitters) in anasynchronous network may be computed in data processing blocks coveringmeasurements obtained in overlapping time periods. In one exampleimplementation, messages containing fine time measurements uploaded frommobile devices may be collected on a regular interval (e.g., one hour).Measurements older than a certain time (e.g., block size) may beexcluded from use in computing m(t), b(t) and Δf(t).

In particular implementations, as discussed above, a server may forwardmessages to mobile devices containing assistance data including, forexample, parameters representing a clock model of timing events at anasynchronous network. Such parameters representing a clock model mayinclude, for example, a fine time assistance frame number (fn_(FTA)), atime reference (t_(FTA)) for the frame number (e.g., time stamp in GPStime), frequency offset estimate (Δf(t)), time uncertainty estimate(σ_(t)) and frequency uncertainty (σ_(t)). A value for fn_(FTA) may becomputed from b(t) and Δf(t) by converting b(t) back to a frame numberwith consideration of a drift in time advance introduced by a frequencyoffset represented by Δf(t) for the time reference (t_(FTA))accordingly. Time reference (t_(FTA)) may represent a time when finetime assistance message is generated or time in the past or future.Here, representing a clock model at least in part with b(t) and Δf(t),we can predict fn_(FTA) for any t_(FTA). For example, if we're trying togenerate an assistance message at 12:00 PM Jan. 1, 2012, we can sett_(FTA)=at 12:00 PM Jan. 1, 2012. Then, we can calculate the acorresponding fn_(FTA). Time reference t_(FTA) may be set as any time inpast, future, or current time. If time reference t_(FTA) is set ascurrent time, a clock model provided in an assistance message may beexpected to be applied at current and future times. Thus, a mobiledevice can use a clock model provided in an assistance messageimmediately upon receipt and for some time in future. Usefulness of aclock model provided in an assistance message may be time-limited aftert_(FTA) and its predication error grows over time. Values for σ_(t) andσ_(t) may be computed as explained below in a non-limiting example.

In a particular implementation, values for computing y=[Δf, b] over atime period containing two or more measurements m (such as a dataprocessing block as discussed above) values may be combined using alinear regression model according to expression (3) as follows:

m=Ty+e _(b)  (3)

where:

${m = \begin{bmatrix}{m\left( t_{0} \right)} & {m\left( t_{1} \right)} & \ldots & {m\left( t_{n - 1} \right)}\end{bmatrix}^{T}};$ ${e_{b} = \begin{bmatrix}{e_{b}\left( t_{0} \right)} & {e_{b}\left( t_{1} \right)} & \ldots & {e_{b}\left( t_{n - 1} \right)}\end{bmatrix}^{T}};$ ${y = \begin{bmatrix}{\Delta \; {f\left( t_{n - 1} \right)}} & {b\left( t_{n - 1} \right)}\end{bmatrix}^{T}};{and}$ $T = {\begin{bmatrix}{t_{0} - t_{n - 1}} & 1 \\{t_{1} - t_{n - 1}} & 1 \\\vdots & \vdots \\{t_{n - 1} - t_{n - 1}} & 1\end{bmatrix}.}$

A linear regression result may then be given in expression (4) asfollows:

ŷ=T ^(†) m  (4)

According to an embodiment, an expression of uncertainty in an estimateof y as function of time b(t) and frequency offset Δf(t) may be computedusing concepts of dilution of precision (DOP), including a time DOP(TDOP) and a frequency DOP (FDOP). Values for TDOP and FDOP may bederived from T in expression (5) as follows:

FDOP=[(T ^(T) T)⁻¹]_(1,1)

TDOP=[(T ^(T) T)⁻¹]_(2,2)  (5)

Uncertainty of time and frequency estimates for a given measurementuncertainty, {circumflex over (σ)}_(m), may be shown in expression (6)as follows:

{circumflex over (σ)}_(f)=FDOP×{circumflex over (σ)}_(m)

{circumflex over (σ)}_(t)=TDOP×{circumflex over (σ)}_(m),  (6)

where {circumflex over (σ)}_(m) may be computed based on a discrepancybetween measurements and an estimated linear model (Δf(t_(n−1)) andb(t_(n−1))) as follows:

${\hat{\sigma}}_{m} = {\sqrt{\frac{1}{n}{\sum_{i = 0}^{n - 1}\left\{ {{m\left( t_{i} \right)} - \left\lbrack {{\hat{b}\left( t_{n - 1} \right)} + {\left( {t_{i} - t_{n - 1}} \right)\hat{\Delta \; f}\left( t_{n - 1} \right)}} \right\rbrack} \right\}^{2}}}.}$

In another embodiment, linear regression results of expression (3) indifferent time intervals (e.g., from different data processing blocks)may be further combined with application of a Kalman filter model. Here,a Kalman filter may consider an intermediate estimate from a robust fit(RF) linear regression model in expression (4),

(t)=[

(t)

(t)]^(T), and generate a combined estimate

(t). Here, such Kalman filter model may be at least partiallycharacterized as follows:

Observation variables:

(t)=[

(t)

(t)]^(T);

State variables:

(t)=[

(t)

(t)]^(T);

Observation model:

${H = \begin{bmatrix}1 & 0 \\0 & 1\end{bmatrix}};$

State transition model:

${A = \begin{bmatrix}1 & 0 \\{\Delta \; t} & 1\end{bmatrix}};$

Observation noise variance:

${R = \begin{bmatrix}{\max \left( {{\hat{\sigma}}_{f,{RF}}^{2},\sigma_{f,{default}}^{2}} \right)} & 0 \\0 & {\max \left( {{\hat{\sigma}}_{t,{RF}}^{2},\sigma_{t,{default}}^{2}} \right)}\end{bmatrix}};$

-   -   and        State noise variance:

$Q = {\begin{bmatrix}\sigma_{f,{state}}^{2} & 0 \\0 & \sigma_{t,{state}}^{2}\end{bmatrix}.}$

At block 126, a server may transmit parameters representative of theclock model computed in block 124 to other mobile devices (e.g., mobiledevices 116) for use in positioning operations as discussed above.

FIG. 4 is a flow diagram of a process obtaining a position fix at amobile device by processing signals observed from a transmitter in anasynchronous network using parameters representing a computed clockmodel (e.g., as computed according to process 120 as described above).As pointed out above, a base station transmitter in an asynchronousnetwork may continuously transmit message frames timed according to aninternal clock (e.g. at a base station transmitter). According to anembodiment, a continuous time model may be constructed from parametersof a computed clock model. Since there may be no time stamps relative toa clock known at a mobile device receiver (e.g., GPS time stamps) onframes transmitted in an asynchronous network, any relationship to sucha clock known at the mobile device may be ambiguous and arbitrary.Furthermore, as pointed out above, there may be an inherent ambiguityfrom an observed number frame of a frame transmitted from thetransmitter in the asynchronous network since a frame number resets tozero after reaching a maximum value in a frame rollover.

At block 136, a mobile device (e.g., a mobile device 116) may acquire asignal transmitted by a transmitter in an asynchronous network (e.g.,base station transmitter in a cellular communication network). Aspointed out above, the mobile device may detect a time reference in theacquired signal such as, for example, a frame boundary. In a particularimplementation, a mobile device may internally maintain a clock model toadvance time and the occurrence of timing events at the asynchronousnetwork. At block 137, a mobile device may update an internal clockmodel representing timing of the time reference in the acquired signalbased, at least in part, on received parameters representing the clockmodel (e.g., transmitted to the mobile device by a server at block 126).For example, the mobile device may attempt to update the internal clockmodel relative to a reliable timing reference controlled according to aknown clock (e.g., GPS time). At block 138, the updated clock model maybe applied to a time reference observed in a signal acquired from atransmitter in an asynchronous network for measuring a range to thetransmitter as part of a positioning operation.

As pointed out above, an accurate comparison of an observed timingreference in a signal acquired from the synchronous network with atiming reference in a signal acquired from an asynchronous network toobtain fine time measurements at a mobile device may depend, at least inpart, on a location of the mobile device. As such, accuracy of fine timemeasurements computed at a mobile device may be affected, at least inpart, on a time uncertainty and/or position uncertainty of the mobiledevice.

In a particular example implementation, a mobile device may obtainapproximation or estimate of its location, u_(approx), and timingreference, t with uncertainty of less than a half of a frame rolloverperiod (3.48 hours in GSM and 40.96 seconds in WCDMA). A distancebetween the mobile device and the transmitter (e.g., base stationtransmitter) located at s_(cell), may be determined from an approximatedsignal as follows:

Δ{circumflex over (t)} _(delay) =∥u _(approx) −s _(cell)∥.

If a value of u_(approx) is not available, a value for Δ{circumflex over(t)}_(delay) may be set to a half of cell radius (e.g., of a basestation in an asynchronous network). A number of frame rolloverinstances, {circumflex over (N)}_(rollover), from a fine time assistancereference time, t_(FTA), may be computed as follows:

${\hat{N}}_{rollover} = \left\lfloor \frac{t_{approx} - \left( {t_{FTA} - {{fn}_{NFA} \times T_{frame}}} \right)}{T_{rollover}} \right\rfloor$

where:

fn_(FTA)=frame number provided in a fine time assistance message att_(ref);

t_(FTA)=reference time of a fine time assistance message;

T_(frame)=time length of a frame; and

T_(rollover)=time length of a frame rollover period.

As shown in FIG. 5 in a particular example, a fine time assistance framenumber fn_(FTA) at time 140 following a rollover event may be propagatedover future rollover events. A network frame number fn(t) observed in asignal from an asynchronous network, at a time 142 after frame rollover,may be converted to a continuous network time, {circumflex over(t)}_(Network)(t) relative to t_(FTA) as follows:

{circumflex over (t)} _(Network)(t)=(fn(t)−fn _(FTA))×T _(frame)+{circumflex over (N)} _(rollover) ×T _(rollover).

A corresponding GPS time, {circumflex over (t)}_(GPS)(t), based on theFTA frequency offset at reference time,

_(FTA), considering time elapse from t_(FTA) and time delay due todistance from the base station transmitter, may be computed as follows:

{circumflex over (t)} _(GPS)(t)=t _(FTA) +{circumflex over (t)}_(Network)(t)×(1−

_(FTA))+Δ{circumflex over (t)} _(delay).

A corresponding uncertainty in {circumflex over (t)}_(GPS) (t), whichmay grow as the FTA reference time after generation of a fine timeassistance message ages over time, may be computed as follows:

${{\hat{\sigma}}_{t}(t)} = {\sqrt{{\hat{\sigma}}_{t,{mobile}}^{2} + {\hat{\sigma}}_{t,{FTA}}^{2} + {\left( {{{\hat{t}}_{GPS}(t)} - t_{FTA}} \right)^{2} \times {\hat{\sigma}}_{f,{FTA}}^{2}}} \approx {{\hat{\sigma}}_{t,{mobile}} + {\left( {{{\hat{t}}_{GPS}(t)} - t_{FTA}} \right) \times {\hat{\sigma}}_{f,{FTA}}}}}$

where:

-   -   {circumflex over (σ)}_(t)(t)=estimated timing uncertainty in        time, t, due to propagation in future,    -   {circumflex over (σ)}_(t,mobile)=estimated timing uncertainty in        time, t, due to mobile's positioning uncertainty (generally,        {circumflex over (σ)}_(t,mobile)>>{circumflex over        (σ)}_(t,FTA)),    -   {circumflex over (σ)}_(t,FTA)=given timing uncertainty from a        FTA message at reference time, t_(FTA),    -   {circumflex over (σ)}_(f,FTA)=given frequency uncertainty from a        FTA message at reference time, t_(FTA).

FIG. 6. Illustrates how an uncertainty 154 in an estimate of GPS timegrows over time from a time reference 156. Line 150 may illustrated anestimated advance of time with respect to known GPS time while lines 152illustrate how an uncertainty in an estimated advance of time increasesover time.

FIG. 7 is a schematic diagram of a mobile device 200 (e.g., used as amobile device 112 or 116 discussed above in FIG. 1). Mobile device 200may comprise any type of wireless communication device, such as awireless telephone, including cordless telephones, cellular telephones,Personal Communication System (“PCS”) telephones, or another type ofwireless telephone. Mobile device 200 may also comprise a two-way radio,such as a walkie-talkie, or other type of communications transceiver.Mobile device 200 may also include circuits to receive and/or transmitBluetooth, 802.11, or other types of wireless signals.

As illustrated, the mobile device architecture 200 may include, forexample, a general purpose processor 202, a digital signal processor204, a wireless transceiver 206, a radio receiver 208, a memory 210, andan SPS receiver 212. A bus 222 or other alternative structure orstructures may be provided for establishing interconnections betweenvarious components of the architecture 200. In the illustratedimplementation, one or more interfaces 214, 216, 218, 220 may beprovided between selected components and bus 222. The wirelesstransceiver 206, the radio receiver 208, and the SPS receiver 212 mayeach be coupled to one or more antennas 224, 226, 228, and/or othertransducers, to facilitate the transmission and/or reception of wirelesssignals.

The general purpose processor 202 and the digital signal processor 204are digital processing devices that are capable of executing programs toprovide one or more functions and/or services to a user. One or both ofthese processors 202, 204 may be used, for example, to execute anoperating system of a corresponding wireless device. One or both ofthese processors 202, 204 may also be used, for example, to execute userapplication programs including, for example, location-based applicationsthat may rely on the availability of an accurate position estimate. Inaddition, one or both of these processors 202, 204 may be used toimplement, either partially or fully, one or more of the positioningrelated processes or techniques described herein in someimplementations. It should be appreciated that other forms of digitalprocessing devices may additionally or alternatively be used to performsome or all of the described functions in various implementationsincluding, for example, one or more controllers, microcontrollers,application specific integrated circuits (ASICs), field programmablegate arrays (FPGAs), programmable logic arrays (PLAs), programmablelogic devices (PLDs), reduced instruction set computers (RISCs), and/orothers, including combinations of the above.

Wireless transceiver 206 may include any type of transceiver that iscapable of supporting wireless communication with one or more remotewireless entities. In various implementations, wireless transceiver 206may be configured in accordance with one or more wireless networkingstandards and/or wireless cellular standards. In some implementations,multiple wireless transceivers may be provided to support operation withdifferent networks or systems in a surrounding environment. Duringmobile device operation, wireless transceiver 206 may be called upon tocommunicate with a base station or access point of a wirelesscommunication system or network. Radio receiver 208 may be operative forreceiving signals from one or more sensors of a sensor network or othertransmitting nodes within a surrounding environment.

Memory 210 may include any type of device or component, or combinationof devices and/or components, that is capable of storing digitalinformation (e.g., digital data, computer executable instructions and/orprograms, etc.) for access by a processing device or other component.This may include, for example, semiconductor memories, magnetic datastorage devices, disc based storage devices, optical storage devices,read only memories (ROMs), random access memories (RAMs), non-volatilememories, flash memories, USB drives, compact disc read only memories(CD-ROMs), DVDs, Blu-Ray disks, magneto-optical disks, erasableprogrammable ROMs (EPROMs), electrically erasable programmable ROMs(EEPROMs), magnetic or optical cards, and/or other digital storagesuitable for storing electronic instructions and/or data.

SPS receiver 212 may include any type of receiver capable of receivingSPS signals from positioning satellites and processing the signals toprovide one or more position estimates for a mobile device. SPS receiver212 may be configured to operate with any existing or future SPS systemincluding, for example, the Global Positioning System (GPS), the GLONASSsystem, the Compass system, the Galileo system, the IRNSS system, theGNSS system and other systems that use Satellite Based AugmentationSystems (SBASs) and/or Ground Based Augmentations Systems (GBASs),and/or other satellite navigation systems. In some implementations, oneor more of the processes or techniques described herein may beimplemented, either partially or fully, within SPS receiver 212 or asimilar structure. It should be appreciated that the mobile devicearchitecture 200 of FIG. 1 represents one possible example of anarchitecture that may be used in a implementation. Other architecturesmay alternatively be used. It should also be appreciated that all orpart of the various devices, processes, or methods described herein maybe implemented using any combination of hardware, firmware, and/orsoftware. FIG. 8 is a schematic diagram illustrating an examplecomputing and communications environment 800 that may include one ormore devices configurable to implement techniques or processes describedabove, for example, in connection with example techniques for computing,updating or applying a clock model. System 800 may include, for example,a first device 802, a second device 804, and a third device 806, whichmay be operatively coupled together through a network 808.

First device 802, second device 804 and third device 806, as shown inFIG. 8, may be representative of any device, appliance or machine thatmay be configurable to exchange data over wireless communicationsnetwork 808. By way of example but not limitation, any of first device802, second device 804, or third device 806 may include: one or morecomputing devices or platforms, such as, e.g., a desktop computer, alaptop computer, a workstation, a server device, or the like; one ormore personal computing or communication devices or appliances, such as,e.g., a personal digital assistant, mobile communication device, or thelike; a computing system or associated service provider capability, suchas, e.g., a database or data storage service provider/system, a networkservice provider/system, an Internet or intranet serviceprovider/system, a portal or search engine service provider/system, awireless communication service provider/system; or any combinationthereof. Any of the first, second, and third devices 802, 804, or 806,respectively, may comprise one or more of an almanac server, an accesspoint, or a mobile station in accordance with the examples describedherein.

Similarly, network 808, as shown in FIG. 8, is representative of one ormore communication links, processes, or resources configurable tosupport the exchange of data between at least two of first device 802,second device 804, and third device 806. By way of example but notlimitation, network 808 may include wireless or wired communicationlinks, telephone or telecommunications systems, data buses or channels,optical fibers, terrestrial or space vehicle resources, local areanetworks, wide area networks, intranets, the Internet, routers orswitches, and the like, or any combination thereof. As illustrated, forexample, by the dashed lined box illustrated as being partially obscuredof third device 806, there may be additional like devices operativelycoupled to network 808.

It is recognized that all or part of the various devices and networksshown in system 800, and the processes and methods as further describedherein, may be implemented using or otherwise including hardware,firmware, software, or any combination thereof.

Thus, by way of example but not limitation, second device 804 mayinclude at least one processing unit 820 that is operatively coupled toa memory 812 through a bus 828.

Processing unit 820 is representative of one or more circuitsconfigurable to perform at least a portion of a data computing procedureor process. By way of example but not limitation, processing unit 820may include one or more processors, controllers, microprocessors,microcontrollers, application specific integrated circuits, digitalsignal processors, programmable logic devices, field programmable gatearrays, and the like, or any combination thereof.

Memory 822 is representative of any data storage mechanism. Memory 822may include, for example, a primary memory 824 or a secondary memory826. Primary memory 824 may include, for example, a random accessmemory, read only memory, etc. While illustrated in this example asbeing separate from processing unit 820, it should be understood thatall or part of primary memory 824 may be provided within or otherwiseco-located/coupled with processing unit 820.

Secondary memory 826 may include, for example, the same or similar typeof memory as primary memory or one or more data storage devices orsystems, such as, for example, a disk drive, an optical disc drive, atape drive, a solid state memory drive, etc. In certain implementations,secondary memory 826 may be operatively receptive of, or otherwiseconfigurable to couple to, a computer-readable medium 840.Computer-readable medium 840 may include, for example, any medium thatcan carry or make accessible data, code or instructions for one or moreof the devices in system 800. Computer readable medium 840 may also bereferred to as a storage medium.

Second device 804 may include, for example, a communication interface830 that provides for or otherwise supports the operative coupling ofsecond device 804 to at least network 808. By way of example but notlimitation, communication interface 830 may include a network interfacedevice or card, a modem, a router, a switch, a transceiver, and thelike.

Second device 804 may include, for example, an input/output 832.Input/output 832 is representative of one or more devices or featuresthat may be configurable to accept or otherwise introduce human ormachine inputs, or one or more devices or features that may beconfigurable to deliver or otherwise provide for human or machineoutputs. By way of example but not limitation, input/output device 832may include an operatively configured display, speaker, keyboard, mouse,trackball, touch screen, data port, etc.

Another position location system that may be used by wireless devices isEnhanced Observed Time Difference (“E-OTD”). E-OTD is a positionlocation system that is optimized for use in Global System for Mobilecommunications (“GSM”) and General Packet Radio Service (“GPRS”)wireless communication systems. In this system, the mobile devicemonitors transmission bursts from multiple base stations and measuresthe time shifts between the arrival of frames in order to determine itsposition. A mobile device may receive signals from three or more basestations to estimate its position. However, the E-OTD system requiresthe use of Location Measurement Units (“LMUs”) strategically placedthroughout the network in order to provide the system with the precisetiming enabling accurate position estimation.

Another position location system that may be used by wireless phones isObserved Time Difference of Arrival (“OTDOA”). OTDOA is a positionlocation system that is optimized for use in Wideband Code DivisionMultiple Access (“WCDMA”) systems. The OTDOA position location systemoperates similar to the E-OTD system. A position of a mobile device maybe estimated by measuring a time difference of arrival of communicationsignals from multiple base stations.

As used herein, the term “mobile device” refers to a device that mayfrom time to time have a position that changes. Such changes in positionmay comprise changes to direction, distance, and/or orientation. Inparticular examples, a mobile device may comprise a cellular telephone,wireless communication device, user equipment, laptop computer, otherpersonal communication system (“PCS”) device, personal digital assistant(“FDA”), personal audio device (“PAD”), portable navigational device, orother portable communication devices. A mobile device may also comprisea processor or computing platform adapted to perform functionscontrolled by machine-readable instructions.

The term “acquire” as used herein as it relates to wireless signalsreceived at a mobile device refers to a mobile device obtainingsufficient signal attributes or symbols from a wireless signal to enableprocessing of the received wireless signal to obtain at least someinformation therein. Example types of information that may be obtainedby a mobile device in acquiring a wireless signal may include, but arenot limited to, carrier frequency, radio-frequency (RF) phase, code,code-phase, timing, messages, transmitter identifier, or Doppler shift,to list but a few examples. Further, it should be noted that the scopeof claimed subject matter is not limited to any particular technique foracquiring a wireless signal.

The methodologies described herein may be implemented by various meansdepending upon applications according to particular examples. Forexample, such methodologies may be implemented in hardware, firmware,software, or combinations thereof. In a hardware implementation, forexample, a processing unit may be implemented within one or moreapplication specific integrated circuits (“ASICs”), digital signalprocessors (“DSPs”), digital signal processing devices (“DSPDs”),programmable logic devices (“PLDs”), field programmable gate arrays(“FPGAs”), processors, controllers, micro-controllers, microprocessors,electronic devices, other devices units designed to perform thefunctions described herein, or combinations thereof.

Some portions of the detailed description included herein are presentedin terms of algorithms or symbolic representations of operations onbinary digital signals stored within a memory of a specific apparatus orspecial purpose computing device or platform. In the context of thisparticular specification, the term specific apparatus or the likeincludes a general purpose computer once it is programmed to performparticular operations pursuant to instructions from program software.Algorithmic descriptions or symbolic representations are examples oftechniques used by those of ordinary skill in the signal processing orrelated arts to convey the substance of their work to others skilled inthe art. An algorithm is here, and generally, is considered to be aself-consistent sequence of operations or similar signal processingleading to a desired result. In this context, operations or processinginvolve physical manipulation of physical quantities. Typically,although not necessarily, such quantities may take the form ofelectrical or magnetic signals capable of being stored, transferred,combined, compared or otherwise manipulated. It has proven convenient attimes, principally for reasons of common usage, to refer to such signalsas bits, data, values, elements, symbols, characters, terms, numbers,numerals, or the like. It should be understood, however, that all ofthese or similar terms are to be associated with appropriate physicalquantities and are merely convenient labels. Unless specifically statedotherwise, as apparent from the discussion herein, it is appreciatedthat throughout this specification discussions utilizing terms such as“processing,” “computing,” “calculating,” “determining” or the likerefer to actions or processes of a specific apparatus, such as a specialpurpose computer or a similar special purpose electronic computingdevice. In the context of this specification, therefore, a specialpurpose computer or a similar special purpose electronic computingdevice is capable of manipulating or transforming signals, typicallyrepresented as physical electronic or magnetic quantities withinmemories, registers, or other information storage devices, transmissiondevices, or display devices of the special purpose computer or similarspecial purpose electronic computing device.

Wireless communication techniques described herein may be in connectionwith various wireless communications networks such as a wireless widearea network (“WWAN”), a wireless local area network (“WLAN”), awireless personal area network (WPAN), and so on. The term “network” and“system” may be used interchangeably herein. A WWAN may be a CodeDivision Multiple Access (“CDMA”) network, a Time Division MultipleAccess (“TDMA”) network, a Frequency Division Multiple Access (“FDMA”)network, an Orthogonal Frequency Division Multiple Access (“OFDMA”)network, a Single-Carrier Frequency Division Multiple Access (“SC-FDMA”)network, or any combination of the above networks, and so on. A CDMAnetwork may implement one or more radio access technologies (“RATs”)such as cdma2000, Wideband-CDMA (“W-CDMA”), to name just a few radiotechnologies. Here, cdma2000 may include technologies implementedaccording to IS-95, IS-2000, and IS-856 standards. A TDMA network mayimplement Global System for Mobile Communications (“GSM”), DigitalAdvanced Mobile Phone System (“D-AMPS”), or some other RAT. GSM andW-CDMA are described in documents from a consortium named “3rdGeneration Partnership Project” (“3GPP”). Cdma2000 is described indocuments from a consortium named “3rd Generation Partnership Project 2”(“3GPP2”). 3GPP and 3GPP2 documents are publicly available. 4G Long TermEvolution (“LTE”) communications networks may also be implemented inaccordance with claimed subject matter, in an aspect. A WLAN maycomprise an IEEE 802.11x network, and a WPAN may comprise a Bluetoothnetwork, an IEEE 802.15x, for example. Wireless communicationimplementations described herein may also be used in connection with anycombination of WWAN, WLAN or WPAN.

In another aspect, as previously mentioned, a wireless transmitter oraccess point may comprise a femtocell, utilized to extend cellulartelephone service into a business or home. In such an implementation,one or more mobile devices may communicate with a femtocell via a codedivision multiple access (“CDMA”) cellular communication protocol, forexample, and the femtocell may provide the mobile device access to alarger cellular telecommunication network by way of another broadbandnetwork such as the Internet.

Techniques described herein may be used with an SPS that includes anyone of several GNSS and/or combinations of GNSS. Furthermore, suchtechniques may be used with positioning systems that utilize terrestrialtransmitters acting as “pseudolites”, or a combination of SVs and suchterrestrial transmitters. Terrestrial transmitters may, for example,include ground-based transmitters that broadcast a PN code or otherranging code (e.g., similar to a GPS or CDMA cellular signal). Such atransmitter may be assigned a unique PN code so as to permitidentification by a remote receiver. Terrestrial transmitters may beuseful, for example, to augment an SPS in situations where SPS signalsfrom an orbiting SV might be unavailable, such as in tunnels, mines,buildings, urban canyons or other enclosed areas. Another implementationof pseudolites is known as radio-beacons. The term “SV”, as used herein,is intended to include terrestrial transmitters acting as pseudolites,equivalents of pseudolites, and possibly others. The terms “SPS signals”and/or “SV signals”, as used herein, is intended to include SPS-likesignals from terrestrial transmitters, including terrestrialtransmitters acting as pseudolites or equivalents of pseudolites.

The terms, “and,” and “or” as used herein may include a variety ofmeanings that will depend at least in part upon the context in which itis used. Typically, “or” if used to associate a list, such as A, B or C,is intended to mean A, B, and C, here used in the inclusive sense, aswell as A, B or C, here used in the exclusive sense. Referencethroughout this specification to “one example” or “an example” meansthat a particular feature, structure, or characteristic described inconnection with the example is included in at least one example ofclaimed subject matter. Thus, the appearances of the phrase “in oneexample” or “an example” in various places throughout this specificationare not necessarily all referring to the same example. Furthermore, theparticular features, structures, or characteristics may be combined inone or more examples. Examples described herein may include machines,devices, engines, or apparatuses that operate using digital signals.Such signals may comprise electronic signals, optical signals,electromagnetic signals, or any form of energy that provides informationbetween locations.

While there has been illustrated and described what are presentlyconsidered to be example features, it will be understood by thoseskilled in the art that various other modifications may be made, andequivalents may be substituted, without departing from claimed subjectmatter. Additionally, many modifications may be made to adapt aparticular situation to the teachings of claimed subject matter withoutdeparting from the central concept described herein. Therefore, it isintended that claimed subject matter not be limited to the particularexamples disclosed, but that such claimed subject matter may alsoinclude all aspects falling within the scope of the appended claims, andequivalents thereof.

1. A method for modeling timing of signals, comprising: receiving fromeach mobile device of one or more mobile devices fine time measurementsdetermined based, at least in part, on a first time reference in one ormore first signals received at the each mobile device from anasynchronous network and a second time reference; computing a clockmodel descriptive of timing of at least one signal transmitted from atransmitter in the asynchronous network based, at least in part, on thefine time measurements, wherein the computed clock model includes atleast one of a clock drift parameter, a clock time uncertainty parameteror a clock frequency uncertainty parameter; and transmitting parametersrepresentative of the computed clock model to one or more receivingmobile devices.
 2. The method of claim 1, wherein the second timereference comprises a time reference obtained from acquisition of asatellite positioning system (SPS) signal.
 3. The method of claim 1,wherein the second time reference comprises a time reference based, atleast in part, on an internal clock of the mobile device.
 4. The methodof claim 1, wherein the fine time measurements comprise at least atime-stamped frame number observed in the one or more first signals, andwherein the clock model further comprises a time offset applied to thetime-stamped frame number.
 5. The method of claim 1, further comprisingweighting the fine time measurements based, at least in part, on atleast one of a position uncertainty or a time uncertainty.
 6. The methodof claim 1, wherein the computed clock model is adapted to predict atiming of a signal in the future.
 7. The method of claim 1, wherein thecomputing the clock model comprises computing the clock model based, atleast in part, on timed batches including fine time measurements.
 8. Themethod of claim 1, wherein the transmitter is a serving base stationhaving a clock, and wherein the computed clock model is representativeof the clock.
 9. An apparatus comprising: a receiver to receive messagesfrom a communication network; a transmitter to transmit messages to thecommunication network; and one or more processors configured to: computea clock model descriptive of timing of at least one signal transmittedin an asynchronous network based, at least in part, on fine timemeasurements received in messages from each mobile device of one or moremobile devices, the clock model being computed based, at least in part,on a first time reference in on or more first signals received at theeach mobile device from the asynchronous network and a second timereference, wherein the computed clock model includes at least one of aclock drift parameter, a clock time uncertainty parameter or a clockfrequency uncertainty parameter; and initiate transmission of messagescontaining parameters representative of the computed clock model throughthe transmitter to one or more receiving mobile devices.
 10. Theapparatus of claim 9, wherein the second time reference comprises a timereference obtained from acquisition of a satellite positioning system(SPS) signal.
 11. The apparatus of claim 9, wherein the fine timemeasurements comprise at least a time-stamped frame number observed inthe one or more first signals.
 12. The apparatus of claim 9, wherein theapparatus is a serving base station having a clock, and wherein thecomputed clock model is representative of the clock.
 13. Anon-transitory storage medium comprising machine-readable code storedthereon which is executable by a special purpose computing apparatus,comprising: code to compute a clock model descriptive of timing of atleast one signal transmitted in an asynchronous network based, at leastin part, on fine time measurements received in messages from each mobiledevice of one or more mobile devices, the fine time measurements beingdetermined based, at least in part, on a first time reference in one ormore first signals received at the each mobile device from theasynchronous network and a second time reference, wherein the computedclock model includes at least one of a clock drift parameter, a clocktime uncertainty parameter or a clock frequency uncertainty parameter;and code to initiate transmission of messages containing parametersrepresentative of the computed clock model to one or more receivingmobile devices.
 14. An apparatus comprising: means for receiving fromeach mobile device of one or more mobile devices fine time measurementsdetermined based, at least in part, on a first time reference in one ormore first signals received at the each mobile device from anasynchronous network and a second time reference; means for computing aclock model descriptive of timing of at least one signal transmittedfrom a transmitter in the asynchronous network based, at least in part,on the fine time measurements, wherein the computed clock model includesat least one of a clock drift parameter, a clock time uncertaintyparameter or a clock frequency uncertainty parameter; and means fortransmitting parameters representative of the computed clock model toone or more receiving mobile devices.